Задание 1. Загрузите датасет insurance_cost.csv

library(readr)
inc <- read_csv("C:/R/insurance_cost.csv")
## Rows: 1338 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): sex, smoker, region
## dbl (4): age, bmi, children, charges
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
head(inc)
## # A tibble: 6 × 7
##     age sex      bmi children smoker region    charges
##   <dbl> <chr>  <dbl>    <dbl> <chr>  <chr>       <dbl>
## 1    19 female  27.9        0 yes    southwest  16885.
## 2    18 male    33.8        1 no     southeast   1726.
## 3    28 male    33          3 no     southeast   4449.
## 4    33 male    22.7        0 no     northwest  21984.
## 5    32 male    28.9        0 no     northwest   3867.
## 6    31 female  25.7        0 no     southeast   3757.
#summary(inc)
#skim(inc)

 

Задание 2. Сделайте интерактивный plotly график отношения индекса массы тела и трат на страховку. Раскрасьте его по колонке smoker

library(plotly)
## Загрузка требуемого пакета: ggplot2
## 
## Присоединяю пакет: 'plotly'
## Следующий объект скрыт от 'package:ggplot2':
## 
##     last_plot
## Следующий объект скрыт от 'package:stats':
## 
##     filter
## Следующий объект скрыт от 'package:graphics':
## 
##     layout
plot_ly(data = inc,
        x = ~ bmi,
        y = ~ charges,
        color = ~smoker)
## No trace type specified:
##   Based on info supplied, a 'scatter' trace seems appropriate.
##   Read more about this trace type -> https://plotly.com/r/reference/#scatter
## No scatter mode specifed:
##   Setting the mode to markers
##   Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode
## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

## Warning in RColorBrewer::brewer.pal(N, "Set2"): minimal value for n is 3, returning requested palette with 3 different levels

 

Задание 3. Сделайте тоже самое через ggplotly

plot <- inc %>% 
  ggplot(aes(x = bmi, 
             y = charges,
             color = smoker)) + 
  geom_point(size = 1) +
  theme_minimal()

ggplotly(plot)

 

Задание 4. Кратко сделайте корреляционный анализ данных insurance_cost. Посмотрите документацию пакетов, которые мы проходили на занятии и, исходя из этого, постройте минимум два новых типа графика (которые мы не строили на занятии)

library(corrplot)
## corrplot 0.92 loaded
inc_clear <- inc %>% 
  select(is.integer | is.numeric)
## Warning: Predicate functions must be wrapped in `where()`.
## 
##   # Bad
##   data %>% select(is.integer)
## 
##   # Good
##   data %>% select(where(is.integer))
## 
## ℹ Please update your code.
## This message is displayed once per session.
## Warning: Predicate functions must be wrapped in `where()`.
## 
##   # Bad
##   data %>% select(is.numeric)
## 
##   # Good
##   data %>% select(where(is.numeric))
## 
## ℹ Please update your code.
## This message is displayed once per session.
inc_cor <- cor(inc_clear)

corrplot(inc_cor, method = 'circle')

corrplot(inc_cor, method = 'ellipse')

 

Задание 5. Превратите все номинативные переменные в бинарные/дамми. Т.е. sex и smoker должны стать бинарными (1/0), а каждое уникальное значение region – отдельной колонкой, где 1 говорит о наличии этого признака для наблюдения, а 0 – об отсутствии. Создайте новый датафрейм, где вы оставите только нумерические переменные.

inc_new <- inc %>%
  mutate(region_n = factor(region, labels = c("1","2","3","4"))) 

inc_new$sex <- ifelse(inc_new$sex == "female", 1, 0)
inc_new$smoker <- ifelse(inc_new$smoker == "yes", 1, 0)

inc_new$region_n <- as.numeric(inc_new$region_n)
inc_new$number <-  c(1:1338)

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ tibble  3.1.7     ✔ dplyr   1.0.9
## ✔ tidyr   1.2.0     ✔ stringr 1.4.0
## ✔ purrr   0.3.4     ✔ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks plotly::filter(), stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
library(dplyr)
library(data.table)
## 
## Присоединяю пакет: 'data.table'
## 
## Следующие объекты скрыты от 'package:dplyr':
## 
##     between, first, last
## 
## Следующий объект скрыт от 'package:purrr':
## 
##     transpose
library(tidyr)

inc_wider <- inc_new %>% 
    arrange(number) %>% 
    mutate(id = rowid(number)) %>%
    pivot_wider(names_from = region, values_from = region_n) %>% 
    select(-id)

inc_wider$number <- NULL

inc_wider <- as.data.frame(inc_wider)

inc_wider$southwest <- as.numeric(unlist(inc_wider$southwest))
inc_wider$southeast <- as.numeric(unlist(inc_wider$southeast))
inc_wider$northwest <- as.numeric(unlist(inc_wider$northwest))
inc_wider$northeast <- as.numeric(unlist(inc_wider$northeast))

inc_wider[is.na(inc_wider)] <- 0

inc_wider <- inc_wider %>% 
  mutate(across(ends_with("st"), ~ ifelse(.>0,1,0))) 

head(inc_wider)
##   age sex    bmi children smoker   charges southwest southeast northwest
## 1  19   1 27.900        0      1 16884.924         1         0         0
## 2  18   0 33.770        1      0  1725.552         0         1         0
## 3  28   0 33.000        3      0  4449.462         0         1         0
## 4  33   0 22.705        0      0 21984.471         0         0         1
## 5  32   0 28.880        0      0  3866.855         0         0         1
## 6  31   1 25.740        0      0  3756.622         0         1         0
##   northeast
## 1         0
## 2         0
## 3         0
## 4         0
## 5         0
## 6         0

 

Задание 6. Постройте иерархическую кластеризацию на этом датафрейме

library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
inc_clear_dist <- dist(inc_wider, method = "euclidean")
as.matrix(inc_clear_dist)[1:6,1:6]
##           1         2          3         4          5          6
## 1     0.000 15159.373 12435.4668  5099.569 13018.0755 13128.3082
## 2 15159.373     0.000  2723.9289 20258.927  2141.3549  2031.1273
## 3 12435.467  2723.929     0.0000 17535.013   582.6445   692.8921
## 4  5099.569 20258.927 17535.0127     0.000 18117.6165 18227.8495
## 5 13018.075  2141.355   582.6445 18117.616     0.0000   110.2964
## 6 13128.308  2031.127   692.8921 18227.849   110.2964     0.0000
inc_clear_hc <- hclust(d = inc_clear_dist, 
                        method = "ward.D2")

fviz_dend(inc_clear_hc, 
          cex = 0.1)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

 

Задание 7. Используя документацию или предложенный учебник сделайте ещё несколько возможных графиков по иерархической кластеризации. Попробуйте раскрасить кластеры разными цветами

#Comparing dendrograms

library(dendextend)
## 
## ---------------------
## Welcome to dendextend version 1.16.0
## Type citation('dendextend') for how to cite the package.
## 
## Type browseVignettes(package = 'dendextend') for the package vignette.
## The github page is: https://github.com/talgalili/dendextend/
## 
## Suggestions and bug-reports can be submitted at: https://github.com/talgalili/dendextend/issues
## You may ask questions at stackoverflow, use the r and dendextend tags: 
##   https://stackoverflow.com/questions/tagged/dendextend
## 
##  To suppress this message use:  suppressPackageStartupMessages(library(dendextend))
## ---------------------
## 
## Присоединяю пакет: 'dendextend'
## Следующий объект скрыт от 'package:data.table':
## 
##     set
## Следующий объект скрыт от 'package:stats':
## 
##     cutree
res.dist <- dist(inc_wider, method = "euclidean")

hc1 <- hclust(res.dist, method = "average")
hc2 <- hclust(res.dist, method = "ward.D2")

dend1 <- as.dendrogram (hc1)
dend2 <- as.dendrogram (hc2)

dend_list <- dendlist(dend1, dend2)

tanglegram(dend1, dend2)

#circular dendrogram

library(factoextra)

inc_clear_dist <- dist(inc_wider, method = "euclidean")
as.matrix(inc_clear_dist)[1:6,1:6]
##           1         2          3         4          5          6
## 1     0.000 15159.373 12435.4668  5099.569 13018.0755 13128.3082
## 2 15159.373     0.000  2723.9289 20258.927  2141.3549  2031.1273
## 3 12435.467  2723.929     0.0000 17535.013   582.6445   692.8921
## 4  5099.569 20258.927 17535.0127     0.000 18117.6165 18227.8495
## 5 13018.075  2141.355   582.6445 18117.616     0.0000   110.2964
## 6 13128.308  2031.127   692.8921 18227.849   110.2964     0.0000
inc_clear_hc <- hclust(d = inc_clear_dist, 
                        method = "ward.D2")

fviz_dend(inc_clear_hc, cex = 0.5, k = 4, k_colors = "jco", type = "circular")
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

#phylogenic trees

library("igraph")
## Warning: пакет 'igraph' был собран под R версии 4.2.2
## 
## Присоединяю пакет: 'igraph'
## Следующие объекты скрыты от 'package:dplyr':
## 
##     as_data_frame, groups, union
## Следующие объекты скрыты от 'package:purrr':
## 
##     compose, simplify
## Следующий объект скрыт от 'package:tidyr':
## 
##     crossing
## Следующий объект скрыт от 'package:tibble':
## 
##     as_data_frame
## Следующий объект скрыт от 'package:plotly':
## 
##     groups
## Следующие объекты скрыты от 'package:stats':
## 
##     decompose, spectrum
## Следующий объект скрыт от 'package:base':
## 
##     union
fviz_dend(inc_clear_hc, k = 4, k_colors = "jco",
type = "phylogenic", repel = TRUE)
## Warning: ggrepel: 1329 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

 

Задание 8. Сделайте одновременный график heatmap и иерархической кластеризации

library(pheatmap)

inc_clear_scaled <- scale(inc_clear)
pheatmap(inc_clear_scaled)

 

Задание 9. Проведите анализ данных полученных в задании 5 методом PCA. Кратко проинтерпретируйте полученные результаты.

inc_pca <- inc_wider %>% 
  select(age, bmi)

ggplot() +
  geom_point(data = inc_pca, aes(x = age, y = bmi)) +
  theme_minimal()

inc_pca <- inc_pca %>% 
  mutate(pc1 = age + bmi)

inc_pca <- inc_pca %>% 
  mutate(pc1_decile = ntile(pc1, 10))

inc_pca <- inc_pca %>% 
  mutate(pc1_decile_ch = case_when(
    pc1_decile == 1 ~ "1",
    (pc1_decile == 5) | (pc1_decile == 6) ~ "5-6",
    pc1_decile == 10 ~ "10"
  ))
inc_pca
##      age    bmi     pc1 pc1_decile pc1_decile_ch
## 1     19 27.900  46.900          1             1
## 2     18 33.770  51.770          2          <NA>
## 3     28 33.000  61.000          4          <NA>
## 4     33 22.705  55.705          3          <NA>
## 5     32 28.880  60.880          4          <NA>
## 6     31 25.740  56.740          3          <NA>
## 7     46 33.440  79.440          7          <NA>
## 8     37 27.740  64.740          4          <NA>
## 9     37 29.830  66.830          5           5-6
## 10    60 25.840  85.840          9          <NA>
## 11    25 26.220  51.220          2          <NA>
## 12    62 26.290  88.290          9          <NA>
## 13    23 34.400  57.400          3          <NA>
## 14    56 39.820  95.820         10            10
## 15    27 42.130  69.130          5           5-6
## 16    19 24.600  43.600          1             1
## 17    52 30.780  82.780          8          <NA>
## 18    23 23.845  46.845          1             1
## 19    56 40.300  96.300         10            10
## 20    30 35.300  65.300          5           5-6
## 21    60 36.005  96.005         10            10
## 22    30 32.400  62.400          4          <NA>
## 23    18 34.100  52.100          2          <NA>
## 24    34 31.920  65.920          5           5-6
## 25    37 28.025  65.025          5           5-6
## 26    59 27.720  86.720          9          <NA>
## 27    63 23.085  86.085          9          <NA>
## 28    55 32.775  87.775          9          <NA>
## 29    23 17.385  40.385          1             1
## 30    31 36.300  67.300          5           5-6
## 31    22 35.600  57.600          3          <NA>
## 32    18 26.315  44.315          1             1
## 33    19 28.600  47.600          1             1
## 34    63 28.310  91.310         10            10
## 35    28 36.400  64.400          4          <NA>
## 36    19 20.425  39.425          1             1
## 37    62 32.965  94.965         10            10
## 38    26 20.800  46.800          1             1
## 39    35 36.670  71.670          6           5-6
## 40    60 39.900  99.900         10            10
## 41    24 26.600  50.600          2          <NA>
## 42    31 36.630  67.630          5           5-6
## 43    41 21.780  62.780          4          <NA>
## 44    37 30.800  67.800          5           5-6
## 45    38 37.050  75.050          7          <NA>
## 46    55 37.300  92.300         10            10
## 47    18 38.665  56.665          3          <NA>
## 48    28 34.770  62.770          4          <NA>
## 49    60 24.530  84.530          8          <NA>
## 50    36 35.200  71.200          6           5-6
## 51    18 35.625  53.625          2          <NA>
## 52    21 33.630  54.630          3          <NA>
## 53    48 28.000  76.000          7          <NA>
## 54    36 34.430  70.430          6           5-6
## 55    40 28.690  68.690          5           5-6
## 56    58 36.955  94.955         10            10
## 57    58 31.825  89.825          9          <NA>
## 58    18 31.680  49.680          2          <NA>
## 59    53 22.880  75.880          7          <NA>
## 60    34 37.335  71.335          6           5-6
## 61    43 27.360  70.360          6           5-6
## 62    25 33.660  58.660          3          <NA>
## 63    64 24.700  88.700          9          <NA>
## 64    28 25.935  53.935          2          <NA>
## 65    20 22.420  42.420          1             1
## 66    19 28.900  47.900          1             1
## 67    61 39.100 100.100         10            10
## 68    40 26.315  66.315          5           5-6
## 69    40 36.190  76.190          7          <NA>
## 70    28 23.980  51.980          2          <NA>
## 71    27 24.750  51.750          2          <NA>
## 72    31 28.500  59.500          4          <NA>
## 73    53 28.100  81.100          8          <NA>
## 74    58 32.010  90.010          9          <NA>
## 75    44 27.400  71.400          6           5-6
## 76    57 34.010  91.010          9          <NA>
## 77    29 29.590  58.590          3          <NA>
## 78    21 35.530  56.530          3          <NA>
## 79    22 39.805  61.805          4          <NA>
## 80    41 32.965  73.965          6           5-6
## 81    31 26.885  57.885          3          <NA>
## 82    45 38.285  83.285          8          <NA>
## 83    22 37.620  59.620          4          <NA>
## 84    48 41.230  89.230          9          <NA>
## 85    37 34.800  71.800          6           5-6
## 86    45 22.895  67.895          5           5-6
## 87    57 31.160  88.160          9          <NA>
## 88    56 27.200  83.200          8          <NA>
## 89    46 27.740  73.740          6           5-6
## 90    55 26.980  81.980          8          <NA>
## 91    21 39.490  60.490          4          <NA>
## 92    53 24.795  77.795          7          <NA>
## 93    59 29.830  88.830          9          <NA>
## 94    35 34.770  69.770          6           5-6
## 95    64 31.300  95.300         10            10
## 96    28 37.620  65.620          5           5-6
## 97    54 30.800  84.800          8          <NA>
## 98    55 38.280  93.280         10            10
## 99    56 19.950  75.950          7          <NA>
## 100   38 19.300  57.300          3          <NA>
## 101   41 31.600  72.600          6           5-6
## 102   30 25.460  55.460          3          <NA>
## 103   18 30.115  48.115          1             1
## 104   61 29.920  90.920          9          <NA>
## 105   34 27.500  61.500          4          <NA>
## 106   20 28.025  48.025          1             1
## 107   19 28.400  47.400          1             1
## 108   26 30.875  56.875          3          <NA>
## 109   29 27.940  56.940          3          <NA>
## 110   63 35.090  98.090         10            10
## 111   54 33.630  87.630          9          <NA>
## 112   55 29.700  84.700          8          <NA>
## 113   37 30.800  67.800          5           5-6
## 114   21 35.720  56.720          3          <NA>
## 115   52 32.205  84.205          8          <NA>
## 116   60 28.595  88.595          9          <NA>
## 117   58 49.060 107.060         10            10
## 118   29 27.940  56.940          3          <NA>
## 119   49 27.170  76.170          7          <NA>
## 120   37 23.370  60.370          4          <NA>
## 121   44 37.100  81.100          8          <NA>
## 122   18 23.750  41.750          1             1
## 123   20 28.975  48.975          1             1
## 124   44 31.350  75.350          7          <NA>
## 125   47 33.915  80.915          8          <NA>
## 126   26 28.785  54.785          3          <NA>
## 127   19 28.300  47.300          1             1
## 128   52 37.400  89.400          9          <NA>
## 129   32 17.765  49.765          2          <NA>
## 130   38 34.700  72.700          6           5-6
## 131   59 26.505  85.505          9          <NA>
## 132   61 22.040  83.040          8          <NA>
## 133   53 35.900  88.900          9          <NA>
## 134   19 25.555  44.555          1             1
## 135   20 28.785  48.785          1             1
## 136   22 28.050  50.050          2          <NA>
## 137   19 34.100  53.100          2          <NA>
## 138   22 25.175  47.175          1             1
## 139   54 31.900  85.900          9          <NA>
## 140   22 36.000  58.000          3          <NA>
## 141   34 22.420  56.420          3          <NA>
## 142   26 32.490  58.490          3          <NA>
## 143   34 25.300  59.300          4          <NA>
## 144   29 29.735  58.735          3          <NA>
## 145   30 28.690  58.690          3          <NA>
## 146   29 38.830  67.830          5           5-6
## 147   46 30.495  76.495          7          <NA>
## 148   51 37.730  88.730          9          <NA>
## 149   53 37.430  90.430          9          <NA>
## 150   19 28.400  47.400          1             1
## 151   35 24.130  59.130          4          <NA>
## 152   48 29.700  77.700          7          <NA>
## 153   32 37.145  69.145          5           5-6
## 154   42 23.370  65.370          5           5-6
## 155   40 25.460  65.460          5           5-6
## 156   44 39.520  83.520          8          <NA>
## 157   48 24.420  72.420          6           5-6
## 158   18 25.175  43.175          1             1
## 159   30 35.530  65.530          5           5-6
## 160   50 27.830  77.830          7          <NA>
## 161   42 26.600  68.600          5           5-6
## 162   18 36.850  54.850          3          <NA>
## 163   54 39.600  93.600         10            10
## 164   32 29.800  61.800          4          <NA>
## 165   37 29.640  66.640          5           5-6
## 166   47 28.215  75.215          7          <NA>
## 167   20 37.000  57.000          3          <NA>
## 168   32 33.155  65.155          5           5-6
## 169   19 31.825  50.825          2          <NA>
## 170   27 18.905  45.905          1             1
## 171   63 41.470 104.470         10            10
## 172   49 30.300  79.300          7          <NA>
## 173   18 15.960  33.960          1             1
## 174   35 34.800  69.800          6           5-6
## 175   24 33.345  57.345          3          <NA>
## 176   63 37.700 100.700         10            10
## 177   38 27.835  65.835          5           5-6
## 178   54 29.200  83.200          8          <NA>
## 179   46 28.900  74.900          6           5-6
## 180   41 33.155  74.155          6           5-6
## 181   58 28.595  86.595          9          <NA>
## 182   18 38.280  56.280          3          <NA>
## 183   22 19.950  41.950          1             1
## 184   44 26.410  70.410          6           5-6
## 185   44 30.690  74.690          6           5-6
## 186   36 41.895  77.895          7          <NA>
## 187   26 29.920  55.920          3          <NA>
## 188   30 30.900  60.900          4          <NA>
## 189   41 32.200  73.200          6           5-6
## 190   29 32.110  61.110          4          <NA>
## 191   61 31.570  92.570         10            10
## 192   36 26.200  62.200          4          <NA>
## 193   25 25.740  50.740          2          <NA>
## 194   56 26.600  82.600          8          <NA>
## 195   18 34.430  52.430          2          <NA>
## 196   19 30.590  49.590          2          <NA>
## 197   39 32.800  71.800          6           5-6
## 198   45 28.600  73.600          6           5-6
## 199   51 18.050  69.050          5           5-6
## 200   64 39.330 103.330         10            10
## 201   19 32.110  51.110          2          <NA>
## 202   48 32.230  80.230          8          <NA>
## 203   60 24.035  84.035          8          <NA>
## 204   27 36.080  63.080          4          <NA>
## 205   46 22.300  68.300          5           5-6
## 206   28 28.880  56.880          3          <NA>
## 207   59 26.400  85.400          9          <NA>
## 208   35 27.740  62.740          4          <NA>
## 209   63 31.800  94.800         10            10
## 210   40 41.230  81.230          8          <NA>
## 211   20 33.000  53.000          2          <NA>
## 212   40 30.875  70.875          6           5-6
## 213   24 28.500  52.500          2          <NA>
## 214   34 26.730  60.730          4          <NA>
## 215   45 30.900  75.900          7          <NA>
## 216   41 37.100  78.100          7          <NA>
## 217   53 26.600  79.600          7          <NA>
## 218   27 23.100  50.100          2          <NA>
## 219   26 29.920  55.920          3          <NA>
## 220   24 23.210  47.210          1             1
## 221   34 33.700  67.700          5           5-6
## 222   53 33.250  86.250          9          <NA>
## 223   32 30.800  62.800          4          <NA>
## 224   19 34.800  53.800          2          <NA>
## 225   42 24.640  66.640          5           5-6
## 226   55 33.880  88.880          9          <NA>
## 227   28 38.060  66.060          5           5-6
## 228   58 41.910  99.910         10            10
## 229   41 31.635  72.635          6           5-6
## 230   47 25.460  72.460          6           5-6
## 231   42 36.195  78.195          7          <NA>
## 232   59 27.830  86.830          9          <NA>
## 233   19 17.800  36.800          1             1
## 234   59 27.500  86.500          9          <NA>
## 235   39 24.510  63.510          4          <NA>
## 236   40 22.220  62.220          4          <NA>
## 237   18 26.730  44.730          1             1
## 238   31 38.390  69.390          5           5-6
## 239   19 29.070  48.070          1             1
## 240   44 38.060  82.060          8          <NA>
## 241   23 36.670  59.670          4          <NA>
## 242   33 22.135  55.135          3          <NA>
## 243   55 26.800  81.800          8          <NA>
## 244   40 35.300  75.300          7          <NA>
## 245   63 27.740  90.740          9          <NA>
## 246   54 30.020  84.020          8          <NA>
## 247   60 38.060  98.060         10            10
## 248   24 35.860  59.860          4          <NA>
## 249   19 20.900  39.900          1             1
## 250   29 28.975  57.975          3          <NA>
## 251   18 17.290  35.290          1             1
## 252   63 32.200  95.200         10            10
## 253   54 34.210  88.210          9          <NA>
## 254   27 30.300  57.300          3          <NA>
## 255   50 31.825  81.825          8          <NA>
## 256   55 25.365  80.365          8          <NA>
## 257   56 33.630  89.630          9          <NA>
## 258   38 40.150  78.150          7          <NA>
## 259   51 24.415  75.415          7          <NA>
## 260   19 31.920  50.920          2          <NA>
## 261   58 25.200  83.200          8          <NA>
## 262   20 26.840  46.840          1             1
## 263   52 24.320  76.320          7          <NA>
## 264   19 36.955  55.955          3          <NA>
## 265   53 38.060  91.060          9          <NA>
## 266   46 42.350  88.350          9          <NA>
## 267   40 19.800  59.800          4          <NA>
## 268   59 32.395  91.395         10            10
## 269   45 30.200  75.200          7          <NA>
## 270   49 25.840  74.840          6           5-6
## 271   18 29.370  47.370          1             1
## 272   50 34.200  84.200          8          <NA>
## 273   41 37.050  78.050          7          <NA>
## 274   50 27.455  77.455          7          <NA>
## 275   25 27.550  52.550          2          <NA>
## 276   47 26.600  73.600          6           5-6
## 277   19 20.615  39.615          1             1
## 278   22 24.300  46.300          1             1
## 279   59 31.790  90.790          9          <NA>
## 280   51 21.560  72.560          6           5-6
## 281   40 28.120  68.120          5           5-6
## 282   54 40.565  94.565         10            10
## 283   30 27.645  57.645          3          <NA>
## 284   55 32.395  87.395          9          <NA>
## 285   52 31.200  83.200          8          <NA>
## 286   46 26.620  72.620          6           5-6
## 287   46 48.070  94.070         10            10
## 288   63 26.220  89.220          9          <NA>
## 289   59 36.765  95.765         10            10
## 290   52 26.400  78.400          7          <NA>
## 291   28 33.400  61.400          4          <NA>
## 292   29 29.640  58.640          3          <NA>
## 293   25 45.540  70.540          6           5-6
## 294   22 28.820  50.820          2          <NA>
## 295   25 26.800  51.800          2          <NA>
## 296   18 22.990  40.990          1             1
## 297   19 27.700  46.700          1             1
## 298   47 25.410  72.410          6           5-6
## 299   31 34.390  65.390          5           5-6
## 300   48 28.880  76.880          7          <NA>
## 301   36 27.550  63.550          4          <NA>
## 302   53 22.610  75.610          7          <NA>
## 303   56 37.510  93.510         10            10
## 304   28 33.000  61.000          4          <NA>
## 305   57 38.000  95.000         10            10
## 306   29 33.345  62.345          4          <NA>
## 307   28 27.500  55.500          3          <NA>
## 308   30 33.330  63.330          4          <NA>
## 309   58 34.865  92.865         10            10
## 310   41 33.060  74.060          6           5-6
## 311   50 26.600  76.600          7          <NA>
## 312   19 24.700  43.700          1             1
## 313   43 35.970  78.970          7          <NA>
## 314   49 35.860  84.860          8          <NA>
## 315   27 31.400  58.400          3          <NA>
## 316   52 33.250  85.250          9          <NA>
## 317   50 32.205  82.205          8          <NA>
## 318   54 32.775  86.775          9          <NA>
## 319   44 27.645  71.645          6           5-6
## 320   32 37.335  69.335          5           5-6
## 321   34 25.270  59.270          4          <NA>
## 322   26 29.640  55.640          3          <NA>
## 323   34 30.800  64.800          4          <NA>
## 324   57 40.945  97.945         10            10
## 325   29 27.200  56.200          3          <NA>
## 326   40 34.105  74.105          6           5-6
## 327   27 23.210  50.210          2          <NA>
## 328   45 36.480  81.480          8          <NA>
## 329   64 33.800  97.800         10            10
## 330   52 36.700  88.700          9          <NA>
## 331   61 36.385  97.385         10            10
## 332   52 27.360  79.360          7          <NA>
## 333   61 31.160  92.160         10            10
## 334   56 28.785  84.785          8          <NA>
## 335   43 35.720  78.720          7          <NA>
## 336   64 34.500  98.500         10            10
## 337   60 25.740  85.740          9          <NA>
## 338   62 27.550  89.550          9          <NA>
## 339   50 32.300  82.300          8          <NA>
## 340   46 27.720  73.720          6           5-6
## 341   24 27.600  51.600          2          <NA>
## 342   62 30.020  92.020         10            10
## 343   60 27.550  87.550          9          <NA>
## 344   63 36.765  99.765         10            10
## 345   49 41.470  90.470          9          <NA>
## 346   34 29.260  63.260          4          <NA>
## 347   33 35.750  68.750          5           5-6
## 348   46 33.345  79.345          7          <NA>
## 349   36 29.920  65.920          5           5-6
## 350   19 27.835  46.835          1             1
## 351   57 23.180  80.180          8          <NA>
## 352   50 25.600  75.600          7          <NA>
## 353   30 27.700  57.700          3          <NA>
## 354   33 35.245  68.245          5           5-6
## 355   18 38.280  56.280          3          <NA>
## 356   46 27.600  73.600          6           5-6
## 357   46 43.890  89.890          9          <NA>
## 358   47 29.830  76.830          7          <NA>
## 359   23 41.910  64.910          4          <NA>
## 360   18 20.790  38.790          1             1
## 361   48 32.300  80.300          8          <NA>
## 362   35 30.500  65.500          5           5-6
## 363   19 21.700  40.700          1             1
## 364   21 26.400  47.400          1             1
## 365   21 21.890  42.890          1             1
## 366   49 30.780  79.780          7          <NA>
## 367   56 32.300  88.300          9          <NA>
## 368   42 24.985  66.985          5           5-6
## 369   44 32.015  76.015          7          <NA>
## 370   18 30.400  48.400          1             1
## 371   61 21.090  82.090          8          <NA>
## 372   57 22.230  79.230          7          <NA>
## 373   42 33.155  75.155          7          <NA>
## 374   26 32.900  58.900          3          <NA>
## 375   20 33.330  53.330          2          <NA>
## 376   23 28.310  51.310          2          <NA>
## 377   39 24.890  63.890          4          <NA>
## 378   24 40.150  64.150          4          <NA>
## 379   64 30.115  94.115         10            10
## 380   62 31.460  93.460         10            10
## 381   27 17.955  44.955          1             1
## 382   55 30.685  85.685          9          <NA>
## 383   55 33.000  88.000          9          <NA>
## 384   35 43.340  78.340          7          <NA>
## 385   44 22.135  66.135          5           5-6
## 386   19 34.400  53.400          2          <NA>
## 387   58 39.050  97.050         10            10
## 388   50 25.365  75.365          7          <NA>
## 389   26 22.610  48.610          1             1
## 390   24 30.210  54.210          2          <NA>
## 391   48 35.625  83.625          8          <NA>
## 392   19 37.430  56.430          3          <NA>
## 393   48 31.445  79.445          7          <NA>
## 394   49 31.350  80.350          8          <NA>
## 395   46 32.300  78.300          7          <NA>
## 396   46 19.855  65.855          5           5-6
## 397   43 34.400  77.400          7          <NA>
## 398   21 31.020  52.020          2          <NA>
## 399   64 25.600  89.600          9          <NA>
## 400   18 38.170  56.170          3          <NA>
## 401   51 20.600  71.600          6           5-6
## 402   47 47.520  94.520         10            10
## 403   64 32.965  96.965         10            10
## 404   49 32.300  81.300          8          <NA>
## 405   31 20.400  51.400          2          <NA>
## 406   52 38.380  90.380          9          <NA>
## 407   33 24.310  57.310          3          <NA>
## 408   47 23.600  70.600          6           5-6
## 409   38 21.120  59.120          4          <NA>
## 410   32 30.030  62.030          4          <NA>
## 411   19 17.480  36.480          1             1
## 412   44 20.235  64.235          4          <NA>
## 413   26 17.195  43.195          1             1
## 414   25 23.900  48.900          1             1
## 415   19 35.150  54.150          2          <NA>
## 416   43 35.640  78.640          7          <NA>
## 417   52 34.100  86.100          9          <NA>
## 418   36 22.600  58.600          3          <NA>
## 419   64 39.160 103.160         10            10
## 420   63 26.980  89.980          9          <NA>
## 421   64 33.880  97.880         10            10
## 422   61 35.860  96.860         10            10
## 423   40 32.775  72.775          6           5-6
## 424   25 30.590  55.590          3          <NA>
## 425   48 30.200  78.200          7          <NA>
## 426   45 24.310  69.310          5           5-6
## 427   38 27.265  65.265          5           5-6
## 428   18 29.165  47.165          1             1
## 429   21 16.815  37.815          1             1
## 430   27 30.400  57.400          3          <NA>
## 431   19 33.100  52.100          2          <NA>
## 432   29 20.235  49.235          2          <NA>
## 433   42 26.900  68.900          5           5-6
## 434   60 30.500  90.500          9          <NA>
## 435   31 28.595  59.595          4          <NA>
## 436   60 33.110  93.110         10            10
## 437   22 31.730  53.730          2          <NA>
## 438   35 28.900  63.900          4          <NA>
## 439   52 46.750  98.750         10            10
## 440   26 29.450  55.450          3          <NA>
## 441   31 32.680  63.680          4          <NA>
## 442   33 33.500  66.500          5           5-6
## 443   18 43.010  61.010          4          <NA>
## 444   59 36.520  95.520         10            10
## 445   56 26.695  82.695          8          <NA>
## 446   45 33.100  78.100          7          <NA>
## 447   60 29.640  89.640          9          <NA>
## 448   56 25.650  81.650          8          <NA>
## 449   40 29.600  69.600          5           5-6
## 450   35 38.600  73.600          6           5-6
## 451   39 29.600  68.600          5           5-6
## 452   30 24.130  54.130          2          <NA>
## 453   24 23.400  47.400          1             1
## 454   20 29.735  49.735          2          <NA>
## 455   32 46.530  78.530          7          <NA>
## 456   59 37.400  96.400         10            10
## 457   55 30.140  85.140          8          <NA>
## 458   57 30.495  87.495          9          <NA>
## 459   56 39.600  95.600         10            10
## 460   40 33.000  73.000          6           5-6
## 461   49 36.630  85.630          9          <NA>
## 462   42 30.000  72.000          6           5-6
## 463   62 38.095 100.095         10            10
## 464   56 25.935  81.935          8          <NA>
## 465   19 25.175  44.175          1             1
## 466   30 28.380  58.380          3          <NA>
## 467   60 28.700  88.700          9          <NA>
## 468   56 33.820  89.820          9          <NA>
## 469   28 24.320  52.320          2          <NA>
## 470   18 24.090  42.090          1             1
## 471   27 32.670  59.670          4          <NA>
## 472   18 30.115  48.115          1             1
## 473   19 29.800  48.800          1             1
## 474   47 33.345  80.345          8          <NA>
## 475   54 25.100  79.100          7          <NA>
## 476   61 28.310  89.310          9          <NA>
## 477   24 28.500  52.500          2          <NA>
## 478   25 35.625  60.625          4          <NA>
## 479   21 36.850  57.850          3          <NA>
## 480   23 32.560  55.560          3          <NA>
## 481   63 41.325 104.325         10            10
## 482   49 37.510  86.510          9          <NA>
## 483   18 31.350  49.350          2          <NA>
## 484   51 39.500  90.500          9          <NA>
## 485   48 34.300  82.300          8          <NA>
## 486   31 31.065  62.065          4          <NA>
## 487   54 21.470  75.470          7          <NA>
## 488   19 28.700  47.700          1             1
## 489   44 38.060  82.060          8          <NA>
## 490   53 31.160  84.160          8          <NA>
## 491   19 32.900  51.900          2          <NA>
## 492   61 25.080  86.080          9          <NA>
## 493   18 25.080  43.080          1             1
## 494   61 43.400 104.400         10            10
## 495   21 25.700  46.700          1             1
## 496   20 27.930  47.930          1             1
## 497   31 23.600  54.600          3          <NA>
## 498   45 28.700  73.700          6           5-6
## 499   44 23.980  67.980          5           5-6
## 500   62 39.200 101.200         10            10
## 501   29 34.400  63.400          4          <NA>
## 502   43 26.030  69.030          5           5-6
## 503   51 23.210  74.210          6           5-6
## 504   19 30.250  49.250          2          <NA>
## 505   38 28.930  66.930          5           5-6
## 506   37 30.875  67.875          5           5-6
## 507   22 31.350  53.350          2          <NA>
## 508   21 23.750  44.750          1             1
## 509   24 25.270  49.270          2          <NA>
## 510   57 28.700  85.700          9          <NA>
## 511   56 32.110  88.110          9          <NA>
## 512   27 33.660  60.660          4          <NA>
## 513   51 22.420  73.420          6           5-6
## 514   19 30.400  49.400          2          <NA>
## 515   39 28.300  67.300          5           5-6
## 516   58 35.700  93.700         10            10
## 517   20 35.310  55.310          3          <NA>
## 518   45 30.495  75.495          7          <NA>
## 519   35 31.000  66.000          5           5-6
## 520   31 30.875  61.875          4          <NA>
## 521   50 27.360  77.360          7          <NA>
## 522   32 44.220  76.220          7          <NA>
## 523   51 33.915  84.915          8          <NA>
## 524   38 37.730  75.730          7          <NA>
## 525   42 26.070  68.070          5           5-6
## 526   18 33.880  51.880          2          <NA>
## 527   19 30.590  49.590          2          <NA>
## 528   51 25.800  76.800          7          <NA>
## 529   46 39.425  85.425          9          <NA>
## 530   18 25.460  43.460          1             1
## 531   57 42.130  99.130         10            10
## 532   62 31.730  93.730         10            10
## 533   59 29.700  88.700          9          <NA>
## 534   37 36.190  73.190          6           5-6
## 535   64 40.480 104.480         10            10
## 536   38 28.025  66.025          5           5-6
## 537   33 38.900  71.900          6           5-6
## 538   46 30.200  76.200          7          <NA>
## 539   46 28.050  74.050          6           5-6
## 540   53 31.350  84.350          8          <NA>
## 541   34 38.000  72.000          6           5-6
## 542   20 31.790  51.790          2          <NA>
## 543   63 36.300  99.300         10            10
## 544   54 47.410 101.410         10            10
## 545   54 30.210  84.210          8          <NA>
## 546   49 25.840  74.840          6           5-6
## 547   28 35.435  63.435          4          <NA>
## 548   54 46.700 100.700         10            10
## 549   25 28.595  53.595          2          <NA>
## 550   43 46.200  89.200          9          <NA>
## 551   63 30.800  93.800         10            10
## 552   32 28.930  60.930          4          <NA>
## 553   62 21.400  83.400          8          <NA>
## 554   52 31.730  83.730          8          <NA>
## 555   25 41.325  66.325          5           5-6
## 556   28 23.800  51.800          2          <NA>
## 557   46 33.440  79.440          7          <NA>
## 558   34 34.210  68.210          5           5-6
## 559   35 34.105  69.105          5           5-6
## 560   19 35.530  54.530          3          <NA>
## 561   46 19.950  65.950          5           5-6
## 562   54 32.680  86.680          9          <NA>
## 563   27 30.500  57.500          3          <NA>
## 564   50 44.770  94.770         10            10
## 565   18 32.120  50.120          2          <NA>
## 566   19 30.495  49.495          2          <NA>
## 567   38 40.565  78.565          7          <NA>
## 568   41 30.590  71.590          6           5-6
## 569   49 31.900  80.900          8          <NA>
## 570   48 40.565  88.565          9          <NA>
## 571   31 29.100  60.100          4          <NA>
## 572   18 37.290  55.290          3          <NA>
## 573   30 43.120  73.120          6           5-6
## 574   62 36.860  98.860         10            10
## 575   57 34.295  91.295         10            10
## 576   58 27.170  85.170          8          <NA>
## 577   22 26.840  48.840          1             1
## 578   31 38.095  69.095          5           5-6
## 579   52 30.200  82.200          8          <NA>
## 580   25 23.465  48.465          1             1
## 581   59 25.460  84.460          8          <NA>
## 582   19 30.590  49.590          2          <NA>
## 583   39 45.430  84.430          8          <NA>
## 584   32 23.650  55.650          3          <NA>
## 585   19 20.700  39.700          1             1
## 586   33 28.270  61.270          4          <NA>
## 587   21 20.235  41.235          1             1
## 588   34 30.210  64.210          4          <NA>
## 589   61 35.910  96.910         10            10
## 590   38 30.690  68.690          5           5-6
## 591   58 29.000  87.000          9          <NA>
## 592   47 19.570  66.570          5           5-6
## 593   20 31.130  51.130          2          <NA>
## 594   21 21.850  42.850          1             1
## 595   41 40.260  81.260          8          <NA>
## 596   46 33.725  79.725          7          <NA>
## 597   42 29.480  71.480          6           5-6
## 598   34 33.250  67.250          5           5-6
## 599   43 32.600  75.600          7          <NA>
## 600   52 37.525  89.525          9          <NA>
## 601   18 39.160  57.160          3          <NA>
## 602   51 31.635  82.635          8          <NA>
## 603   56 25.300  81.300          8          <NA>
## 604   64 39.050 103.050         10            10
## 605   19 28.310  47.310          1             1
## 606   51 34.100  85.100          8          <NA>
## 607   27 25.175  52.175          2          <NA>
## 608   59 23.655  82.655          8          <NA>
## 609   28 26.980  54.980          3          <NA>
## 610   30 37.800  67.800          5           5-6
## 611   47 29.370  76.370          7          <NA>
## 612   38 34.800  72.800          6           5-6
## 613   18 33.155  51.155          2          <NA>
## 614   34 19.000  53.000          2          <NA>
## 615   20 33.000  53.000          2          <NA>
## 616   47 36.630  83.630          8          <NA>
## 617   56 28.595  84.595          8          <NA>
## 618   49 25.600  74.600          6           5-6
## 619   19 33.110  52.110          2          <NA>
## 620   55 37.100  92.100         10            10
## 621   30 31.400  61.400          4          <NA>
## 622   37 34.100  71.100          6           5-6
## 623   49 21.300  70.300          6           5-6
## 624   18 33.535  51.535          2          <NA>
## 625   59 28.785  87.785          9          <NA>
## 626   29 26.030  55.030          3          <NA>
## 627   36 28.880  64.880          4          <NA>
## 628   33 42.460  75.460          7          <NA>
## 629   58 38.000  96.000         10            10
## 630   44 38.950  82.950          8          <NA>
## 631   53 36.100  89.100          9          <NA>
## 632   24 29.300  53.300          2          <NA>
## 633   29 35.530  64.530          4          <NA>
## 634   40 22.705  62.705          4          <NA>
## 635   51 39.700  90.700          9          <NA>
## 636   64 38.190 102.190         10            10
## 637   19 24.510  43.510          1             1
## 638   35 38.095  73.095          6           5-6
## 639   39 26.410  65.410          5           5-6
## 640   56 33.660  89.660          9          <NA>
## 641   33 42.400  75.400          7          <NA>
## 642   42 28.310  70.310          6           5-6
## 643   61 33.915  94.915         10            10
## 644   23 34.960  57.960          3          <NA>
## 645   43 35.310  78.310          7          <NA>
## 646   48 30.780  78.780          7          <NA>
## 647   39 26.220  65.220          5           5-6
## 648   40 23.370  63.370          4          <NA>
## 649   18 28.500  46.500          1             1
## 650   58 32.965  90.965          9          <NA>
## 651   49 42.680  91.680         10            10
## 652   53 39.600  92.600         10            10
## 653   48 31.130  79.130          7          <NA>
## 654   45 36.300  81.300          8          <NA>
## 655   59 35.200  94.200         10            10
## 656   52 25.300  77.300          7          <NA>
## 657   26 42.400  68.400          5           5-6
## 658   27 33.155  60.155          4          <NA>
## 659   48 35.910  83.910          8          <NA>
## 660   57 28.785  85.785          9          <NA>
## 661   37 46.530  83.530          8          <NA>
## 662   57 23.980  80.980          8          <NA>
## 663   32 31.540  63.540          4          <NA>
## 664   18 33.660  51.660          2          <NA>
## 665   64 22.990  86.990          9          <NA>
## 666   43 38.060  81.060          8          <NA>
## 667   49 28.700  77.700          7          <NA>
## 668   40 32.775  72.775          6           5-6
## 669   62 32.015  94.015         10            10
## 670   40 29.810  69.810          6           5-6
## 671   30 31.570  61.570          4          <NA>
## 672   29 31.160  60.160          4          <NA>
## 673   36 29.700  65.700          5           5-6
## 674   41 31.020  72.020          6           5-6
## 675   44 43.890  87.890          9          <NA>
## 676   45 21.375  66.375          5           5-6
## 677   55 40.810  95.810         10            10
## 678   60 31.350  91.350         10            10
## 679   56 36.100  92.100         10            10
## 680   49 23.180  72.180          6           5-6
## 681   21 17.400  38.400          1             1
## 682   19 20.300  39.300          1             1
## 683   39 35.300  74.300          6           5-6
## 684   53 24.320  77.320          7          <NA>
## 685   33 18.500  51.500          2          <NA>
## 686   53 26.410  79.410          7          <NA>
## 687   42 26.125  68.125          5           5-6
## 688   40 41.690  81.690          8          <NA>
## 689   47 24.100  71.100          6           5-6
## 690   27 31.130  58.130          3          <NA>
## 691   21 27.360  48.360          1             1
## 692   47 36.200  83.200          8          <NA>
## 693   20 32.395  52.395          2          <NA>
## 694   24 23.655  47.655          1             1
## 695   27 34.800  61.800          4          <NA>
## 696   26 40.185  66.185          5           5-6
## 697   53 32.300  85.300          9          <NA>
## 698   41 35.750  76.750          7          <NA>
## 699   56 33.725  89.725          9          <NA>
## 700   23 39.270  62.270          4          <NA>
## 701   21 34.870  55.870          3          <NA>
## 702   50 44.745  94.745         10            10
## 703   53 41.470  94.470         10            10
## 704   34 26.410  60.410          4          <NA>
## 705   47 29.545  76.545          7          <NA>
## 706   33 32.900  65.900          5           5-6
## 707   51 38.060  89.060          9          <NA>
## 708   49 28.690  77.690          7          <NA>
## 709   31 30.495  61.495          4          <NA>
## 710   36 27.740  63.740          4          <NA>
## 711   18 35.200  53.200          2          <NA>
## 712   50 23.540  73.540          6           5-6
## 713   43 30.685  73.685          6           5-6
## 714   20 40.470  60.470          4          <NA>
## 715   24 22.600  46.600          1             1
## 716   60 28.900  88.900          9          <NA>
## 717   49 22.610  71.610          6           5-6
## 718   60 24.320  84.320          8          <NA>
## 719   51 36.670  87.670          9          <NA>
## 720   58 33.440  91.440         10            10
## 721   51 40.660  91.660         10            10
## 722   53 36.600  89.600          9          <NA>
## 723   62 37.400  99.400         10            10
## 724   19 35.400  54.400          3          <NA>
## 725   50 27.075  77.075          7          <NA>
## 726   30 39.050  69.050          5           5-6
## 727   41 28.405  69.405          5           5-6
## 728   29 21.755  50.755          2          <NA>
## 729   18 40.280  58.280          3          <NA>
## 730   41 36.080  77.080          7          <NA>
## 731   35 24.420  59.420          4          <NA>
## 732   53 21.400  74.400          6           5-6
## 733   24 30.100  54.100          2          <NA>
## 734   48 27.265  75.265          7          <NA>
## 735   59 32.100  91.100          9          <NA>
## 736   49 34.770  83.770          8          <NA>
## 737   37 38.390  75.390          7          <NA>
## 738   26 23.700  49.700          2          <NA>
## 739   23 31.730  54.730          3          <NA>
## 740   29 35.500  64.500          4          <NA>
## 741   45 24.035  69.035          5           5-6
## 742   27 29.150  56.150          3          <NA>
## 743   53 34.105  87.105          9          <NA>
## 744   31 26.620  57.620          3          <NA>
## 745   50 26.410  76.410          7          <NA>
## 746   50 30.115  80.115          8          <NA>
## 747   34 27.000  61.000          4          <NA>
## 748   19 21.755  40.755          1             1
## 749   47 36.000  83.000          8          <NA>
## 750   28 30.875  58.875          3          <NA>
## 751   37 26.400  63.400          4          <NA>
## 752   21 28.975  49.975          2          <NA>
## 753   64 37.905 101.905         10            10
## 754   58 22.770  80.770          8          <NA>
## 755   24 33.630  57.630          3          <NA>
## 756   31 27.645  58.645          3          <NA>
## 757   39 22.800  61.800          4          <NA>
## 758   47 27.830  74.830          6           5-6
## 759   30 37.430  67.430          5           5-6
## 760   18 38.170  56.170          3          <NA>
## 761   22 34.580  56.580          3          <NA>
## 762   23 35.200  58.200          3          <NA>
## 763   33 27.100  60.100          4          <NA>
## 764   27 26.030  53.030          2          <NA>
## 765   45 25.175  70.175          6           5-6
## 766   57 31.825  88.825          9          <NA>
## 767   47 32.300  79.300          7          <NA>
## 768   42 29.000  71.000          6           5-6
## 769   64 39.700 103.700         10            10
## 770   38 19.475  57.475          3          <NA>
## 771   61 36.100  97.100         10            10
## 772   53 26.700  79.700          7          <NA>
## 773   44 36.480  80.480          8          <NA>
## 774   19 28.880  47.880          1             1
## 775   41 34.200  75.200          7          <NA>
## 776   51 33.330  84.330          8          <NA>
## 777   40 32.300  72.300          6           5-6
## 778   45 39.805  84.805          8          <NA>
## 779   35 34.320  69.320          5           5-6
## 780   53 28.880  81.880          8          <NA>
## 781   30 24.400  54.400          3          <NA>
## 782   18 41.140  59.140          4          <NA>
## 783   51 35.970  86.970          9          <NA>
## 784   50 27.600  77.600          7          <NA>
## 785   31 29.260  60.260          4          <NA>
## 786   35 27.700  62.700          4          <NA>
## 787   60 36.955  96.955         10            10
## 788   21 36.860  57.860          3          <NA>
## 789   29 22.515  51.515          2          <NA>
## 790   62 29.920  91.920         10            10
## 791   39 41.800  80.800          8          <NA>
## 792   19 27.600  46.600          1             1
## 793   22 23.180  45.180          1             1
## 794   53 20.900  73.900          6           5-6
## 795   39 31.920  70.920          6           5-6
## 796   27 28.500  55.500          3          <NA>
## 797   30 44.220  74.220          6           5-6
## 798   30 22.895  52.895          2          <NA>
## 799   58 33.100  91.100         10            10
## 800   33 24.795  57.795          3          <NA>
## 801   42 26.180  68.180          5           5-6
## 802   64 35.970  99.970         10            10
## 803   21 22.300  43.300          1             1
## 804   18 42.240  60.240          4          <NA>
## 805   23 26.510  49.510          2          <NA>
## 806   45 35.815  80.815          8          <NA>
## 807   40 41.420  81.420          8          <NA>
## 808   19 36.575  55.575          3          <NA>
## 809   18 30.140  48.140          1             1
## 810   25 25.840  50.840          2          <NA>
## 811   46 30.800  76.800          7          <NA>
## 812   33 42.940  75.940          7          <NA>
## 813   54 21.010  75.010          6           5-6
## 814   28 22.515  50.515          2          <NA>
## 815   36 34.430  70.430          6           5-6
## 816   20 31.460  51.460          2          <NA>
## 817   24 24.225  48.225          1             1
## 818   23 37.100  60.100          4          <NA>
## 819   47 26.125  73.125          6           5-6
## 820   33 35.530  68.530          5           5-6
## 821   45 33.700  78.700          7          <NA>
## 822   26 17.670  43.670          1             1
## 823   18 31.130  49.130          2          <NA>
## 824   44 29.810  73.810          6           5-6
## 825   60 24.320  84.320          8          <NA>
## 826   64 31.825  95.825         10            10
## 827   56 31.790  87.790          9          <NA>
## 828   36 28.025  64.025          4          <NA>
## 829   41 30.780  71.780          6           5-6
## 830   39 21.850  60.850          4          <NA>
## 831   63 33.100  96.100         10            10
## 832   36 25.840  61.840          4          <NA>
## 833   28 23.845  51.845          2          <NA>
## 834   58 34.390  92.390         10            10
## 835   36 33.820  69.820          6           5-6
## 836   42 35.970  77.970          7          <NA>
## 837   36 31.500  67.500          5           5-6
## 838   56 28.310  84.310          8          <NA>
## 839   35 23.465  58.465          3          <NA>
## 840   59 31.350  90.350          9          <NA>
## 841   21 31.100  52.100          2          <NA>
## 842   59 24.700  83.700          8          <NA>
## 843   23 32.780  55.780          3          <NA>
## 844   57 29.810  86.810          9          <NA>
## 845   53 30.495  83.495          8          <NA>
## 846   60 32.450  92.450         10            10
## 847   51 34.200  85.200          8          <NA>
## 848   23 50.380  73.380          6           5-6
## 849   27 24.100  51.100          2          <NA>
## 850   55 32.775  87.775          9          <NA>
## 851   37 30.780  67.780          5           5-6
## 852   61 32.300  93.300         10            10
## 853   46 35.530  81.530          8          <NA>
## 854   53 23.750  76.750          7          <NA>
## 855   49 23.845  72.845          6           5-6
## 856   20 29.600  49.600          2          <NA>
## 857   48 33.110  81.110          8          <NA>
## 858   25 24.130  49.130          2          <NA>
## 859   25 32.230  57.230          3          <NA>
## 860   57 28.100  85.100          8          <NA>
## 861   37 47.600  84.600          8          <NA>
## 862   38 28.000  66.000          5           5-6
## 863   55 33.535  88.535          9          <NA>
## 864   36 19.855  55.855          3          <NA>
## 865   51 25.400  76.400          7          <NA>
## 866   40 29.900  69.900          6           5-6
## 867   18 37.290  55.290          3          <NA>
## 868   57 43.700 100.700         10            10
## 869   61 23.655  84.655          8          <NA>
## 870   25 24.300  49.300          2          <NA>
## 871   50 36.200  86.200          9          <NA>
## 872   26 29.480  55.480          3          <NA>
## 873   42 24.860  66.860          5           5-6
## 874   43 30.100  73.100          6           5-6
## 875   44 21.850  65.850          5           5-6
## 876   23 28.120  51.120          2          <NA>
## 877   49 27.100  76.100          7          <NA>
## 878   33 33.440  66.440          5           5-6
## 879   41 28.800  69.800          6           5-6
## 880   37 29.500  66.500          5           5-6
## 881   22 34.800  56.800          3          <NA>
## 882   23 27.360  50.360          2          <NA>
## 883   21 22.135  43.135          1             1
## 884   51 37.050  88.050          9          <NA>
## 885   25 26.695  51.695          2          <NA>
## 886   32 28.930  60.930          4          <NA>
## 887   57 28.975  85.975          9          <NA>
## 888   36 30.020  66.020          5           5-6
## 889   22 39.500  61.500          4          <NA>
## 890   57 33.630  90.630          9          <NA>
## 891   64 26.885  90.885          9          <NA>
## 892   36 29.040  65.040          5           5-6
## 893   54 24.035  78.035          7          <NA>
## 894   47 38.940  85.940          9          <NA>
## 895   62 32.110  94.110         10            10
## 896   61 44.000 105.000         10            10
## 897   43 20.045  63.045          4          <NA>
## 898   19 25.555  44.555          1             1
## 899   18 40.260  58.260          3          <NA>
## 900   19 22.515  41.515          1             1
## 901   49 22.515  71.515          6           5-6
## 902   60 40.920 100.920         10            10
## 903   26 27.265  53.265          2          <NA>
## 904   49 36.850  85.850          9          <NA>
## 905   60 35.100  95.100         10            10
## 906   26 29.355  55.355          3          <NA>
## 907   27 32.585  59.585          4          <NA>
## 908   44 32.340  76.340          7          <NA>
## 909   63 39.800 102.800         10            10
## 910   32 24.600  56.600          3          <NA>
## 911   22 28.310  50.310          2          <NA>
## 912   18 31.730  49.730          2          <NA>
## 913   59 26.695  85.695          9          <NA>
## 914   44 27.500  71.500          6           5-6
## 915   33 24.605  57.605          3          <NA>
## 916   24 33.990  57.990          3          <NA>
## 917   43 26.885  69.885          6           5-6
## 918   45 22.895  67.895          5           5-6
## 919   61 28.200  89.200          9          <NA>
## 920   35 34.210  69.210          5           5-6
## 921   62 25.000  87.000          9          <NA>
## 922   62 33.200  95.200         10            10
## 923   38 31.000  69.000          5           5-6
## 924   34 35.815  69.815          6           5-6
## 925   43 23.200  66.200          5           5-6
## 926   50 32.110  82.110          8          <NA>
## 927   19 23.400  42.400          1             1
## 928   57 20.100  77.100          7          <NA>
## 929   62 39.160 101.160         10            10
## 930   41 34.210  75.210          7          <NA>
## 931   26 46.530  72.530          6           5-6
## 932   39 32.500  71.500          6           5-6
## 933   46 25.800  71.800          6           5-6
## 934   45 35.300  80.300          8          <NA>
## 935   32 37.180  69.180          5           5-6
## 936   59 27.500  86.500          9          <NA>
## 937   44 29.735  73.735          6           5-6
## 938   39 24.225  63.225          4          <NA>
## 939   18 26.180  44.180          1             1
## 940   53 29.480  82.480          8          <NA>
## 941   18 23.210  41.210          1             1
## 942   50 46.090  96.090         10            10
## 943   18 40.185  58.185          3          <NA>
## 944   19 22.610  41.610          1             1
## 945   62 39.930 101.930         10            10
## 946   56 35.800  91.800         10            10
## 947   42 35.800  77.800          7          <NA>
## 948   37 34.200  71.200          6           5-6
## 949   42 31.255  73.255          6           5-6
## 950   25 29.700  54.700          3          <NA>
## 951   57 18.335  75.335          7          <NA>
## 952   51 42.900  93.900         10            10
## 953   30 28.405  58.405          3          <NA>
## 954   44 30.200  74.200          6           5-6
## 955   34 27.835  61.835          4          <NA>
## 956   31 39.490  70.490          6           5-6
## 957   54 30.800  84.800          8          <NA>
## 958   24 26.790  50.790          2          <NA>
## 959   43 34.960  77.960          7          <NA>
## 960   48 36.670  84.670          8          <NA>
## 961   19 39.615  58.615          3          <NA>
## 962   29 25.900  54.900          3          <NA>
## 963   63 35.200  98.200         10            10
## 964   46 24.795  70.795          6           5-6
## 965   52 36.765  88.765          9          <NA>
## 966   35 27.100  62.100          4          <NA>
## 967   51 24.795  75.795          7          <NA>
## 968   44 25.365  69.365          5           5-6
## 969   21 25.745  46.745          1             1
## 970   39 34.320  73.320          6           5-6
## 971   50 28.160  78.160          7          <NA>
## 972   34 23.560  57.560          3          <NA>
## 973   22 20.235  42.235          1             1
## 974   19 40.500  59.500          4          <NA>
## 975   26 35.420  61.420          4          <NA>
## 976   29 22.895  51.895          2          <NA>
## 977   48 40.150  88.150          9          <NA>
## 978   26 29.150  55.150          3          <NA>
## 979   45 39.995  84.995          8          <NA>
## 980   36 29.920  65.920          5           5-6
## 981   54 25.460  79.460          7          <NA>
## 982   34 21.375  55.375          3          <NA>
## 983   31 25.900  56.900          3          <NA>
## 984   27 30.590  57.590          3          <NA>
## 985   20 30.115  50.115          2          <NA>
## 986   44 25.800  69.800          6           5-6
## 987   43 30.115  73.115          6           5-6
## 988   45 27.645  72.645          6           5-6
## 989   34 34.675  68.675          5           5-6
## 990   24 20.520  44.520          1             1
## 991   26 19.800  45.800          1             1
## 992   38 27.835  65.835          5           5-6
## 993   50 31.600  81.600          8          <NA>
## 994   38 28.270  66.270          5           5-6
## 995   27 20.045  47.045          1             1
## 996   39 23.275  62.275          4          <NA>
## 997   39 34.100  73.100          6           5-6
## 998   63 36.850  99.850         10            10
## 999   33 36.290  69.290          5           5-6
## 1000  36 26.885  62.885          4          <NA>
## 1001  30 22.990  52.990          2          <NA>
## 1002  24 32.700  56.700          3          <NA>
## 1003  24 25.800  49.800          2          <NA>
## 1004  48 29.600  77.600          7          <NA>
## 1005  47 19.190  66.190          5           5-6
## 1006  29 31.730  60.730          4          <NA>
## 1007  28 29.260  57.260          3          <NA>
## 1008  47 28.215  75.215          7          <NA>
## 1009  25 24.985  49.985          2          <NA>
## 1010  51 27.740  78.740          7          <NA>
## 1011  48 22.800  70.800          6           5-6
## 1012  43 20.130  63.130          4          <NA>
## 1013  61 33.330  94.330         10            10
## 1014  48 32.300  80.300          8          <NA>
## 1015  38 27.600  65.600          5           5-6
## 1016  59 25.460  84.460          8          <NA>
## 1017  19 24.605  43.605          1             1
## 1018  26 34.200  60.200          4          <NA>
## 1019  54 35.815  89.815          9          <NA>
## 1020  21 32.680  53.680          2          <NA>
## 1021  51 37.000  88.000          9          <NA>
## 1022  22 31.020  53.020          2          <NA>
## 1023  47 36.080  83.080          8          <NA>
## 1024  18 23.320  41.320          1             1
## 1025  47 45.320  92.320         10            10
## 1026  21 34.600  55.600          3          <NA>
## 1027  19 26.030  45.030          1             1
## 1028  23 18.715  41.715          1             1
## 1029  54 31.600  85.600          9          <NA>
## 1030  37 17.290  54.290          2          <NA>
## 1031  46 23.655  69.655          6           5-6
## 1032  55 35.200  90.200          9          <NA>
## 1033  30 27.930  57.930          3          <NA>
## 1034  18 21.565  39.565          1             1
## 1035  61 38.380  99.380         10            10
## 1036  54 23.000  77.000          7          <NA>
## 1037  22 37.070  59.070          4          <NA>
## 1038  45 30.495  75.495          7          <NA>
## 1039  22 28.880  50.880          2          <NA>
## 1040  19 27.265  46.265          1             1
## 1041  35 28.025  63.025          4          <NA>
## 1042  18 23.085  41.085          1             1
## 1043  20 30.685  50.685          2          <NA>
## 1044  28 25.800  53.800          2          <NA>
## 1045  55 35.245  90.245          9          <NA>
## 1046  43 24.700  67.700          5           5-6
## 1047  43 25.080  68.080          5           5-6
## 1048  22 52.580  74.580          6           5-6
## 1049  25 22.515  47.515          1             1
## 1050  49 30.900  79.900          7          <NA>
## 1051  44 36.955  80.955          8          <NA>
## 1052  64 26.410  90.410          9          <NA>
## 1053  49 29.830  78.830          7          <NA>
## 1054  47 29.800  76.800          7          <NA>
## 1055  27 21.470  48.470          1             1
## 1056  55 27.645  82.645          8          <NA>
## 1057  48 28.900  76.900          7          <NA>
## 1058  45 31.790  76.790          7          <NA>
## 1059  24 39.490  63.490          4          <NA>
## 1060  32 33.820  65.820          5           5-6
## 1061  24 32.010  56.010          3          <NA>
## 1062  57 27.940  84.940          8          <NA>
## 1063  59 41.140 100.140         10            10
## 1064  36 28.595  64.595          4          <NA>
## 1065  29 25.600  54.600          3          <NA>
## 1066  42 25.300  67.300          5           5-6
## 1067  48 37.290  85.290          9          <NA>
## 1068  39 42.655  81.655          8          <NA>
## 1069  63 21.660  84.660          8          <NA>
## 1070  54 31.900  85.900          9          <NA>
## 1071  37 37.070  74.070          6           5-6
## 1072  63 31.445  94.445         10            10
## 1073  21 31.255  52.255          2          <NA>
## 1074  54 28.880  82.880          8          <NA>
## 1075  60 18.335  78.335          7          <NA>
## 1076  32 29.590  61.590          4          <NA>
## 1077  47 32.000  79.000          7          <NA>
## 1078  21 26.030  47.030          1             1
## 1079  28 31.680  59.680          4          <NA>
## 1080  63 33.660  96.660         10            10
## 1081  18 21.780  39.780          1             1
## 1082  32 27.835  59.835          4          <NA>
## 1083  38 19.950  57.950          3          <NA>
## 1084  32 31.500  63.500          4          <NA>
## 1085  62 30.495  92.495         10            10
## 1086  39 18.300  57.300          3          <NA>
## 1087  55 28.975  83.975          8          <NA>
## 1088  57 31.540  88.540          9          <NA>
## 1089  52 47.740  99.740         10            10
## 1090  56 22.100  78.100          7          <NA>
## 1091  47 36.190  83.190          8          <NA>
## 1092  55 29.830  84.830          8          <NA>
## 1093  23 32.700  55.700          3          <NA>
## 1094  22 30.400  52.400          2          <NA>
## 1095  50 33.700  83.700          8          <NA>
## 1096  18 31.350  49.350          2          <NA>
## 1097  51 34.960  85.960          9          <NA>
## 1098  22 33.770  55.770          3          <NA>
## 1099  52 30.875  82.875          8          <NA>
## 1100  25 33.990  58.990          3          <NA>
## 1101  33 19.095  52.095          2          <NA>
## 1102  53 28.600  81.600          8          <NA>
## 1103  29 38.940  67.940          5           5-6
## 1104  58 36.080  94.080         10            10
## 1105  37 29.800  66.800          5           5-6
## 1106  54 31.240  85.240          8          <NA>
## 1107  49 29.925  78.925          7          <NA>
## 1108  50 26.220  76.220          7          <NA>
## 1109  26 30.000  56.000          3          <NA>
## 1110  45 20.350  65.350          5           5-6
## 1111  54 32.300  86.300          9          <NA>
## 1112  38 38.390  76.390          7          <NA>
## 1113  48 25.850  73.850          6           5-6
## 1114  28 26.315  54.315          2          <NA>
## 1115  23 24.510  47.510          1             1
## 1116  55 32.670  87.670          9          <NA>
## 1117  41 29.640  70.640          6           5-6
## 1118  25 33.330  58.330          3          <NA>
## 1119  33 35.750  68.750          5           5-6
## 1120  30 19.950  49.950          2          <NA>
## 1121  23 31.400  54.400          3          <NA>
## 1122  46 38.170  84.170          8          <NA>
## 1123  53 36.860  89.860          9          <NA>
## 1124  27 32.395  59.395          4          <NA>
## 1125  23 42.750  65.750          5           5-6
## 1126  63 25.080  88.080          9          <NA>
## 1127  55 29.900  84.900          8          <NA>
## 1128  35 35.860  70.860          6           5-6
## 1129  34 32.800  66.800          5           5-6
## 1130  19 18.600  37.600          1             1
## 1131  39 23.870  62.870          4          <NA>
## 1132  27 45.900  72.900          6           5-6
## 1133  57 40.280  97.280         10            10
## 1134  52 18.335  70.335          6           5-6
## 1135  28 33.820  61.820          4          <NA>
## 1136  50 28.120  78.120          7          <NA>
## 1137  44 25.000  69.000          5           5-6
## 1138  26 22.230  48.230          1             1
## 1139  33 30.250  63.250          4          <NA>
## 1140  19 32.490  51.490          2          <NA>
## 1141  50 37.070  87.070          9          <NA>
## 1142  41 32.600  73.600          6           5-6
## 1143  52 24.860  76.860          7          <NA>
## 1144  39 32.340  71.340          6           5-6
## 1145  50 32.300  82.300          8          <NA>
## 1146  52 32.775  84.775          8          <NA>
## 1147  60 32.800  92.800         10            10
## 1148  20 31.920  51.920          2          <NA>
## 1149  55 21.500  76.500          7          <NA>
## 1150  42 34.100  76.100          7          <NA>
## 1151  18 30.305  48.305          1             1
## 1152  58 36.480  94.480         10            10
## 1153  43 32.560  75.560          7          <NA>
## 1154  35 35.815  70.815          6           5-6
## 1155  48 27.930  75.930          7          <NA>
## 1156  36 22.135  58.135          3          <NA>
## 1157  19 44.880  63.880          4          <NA>
## 1158  23 23.180  46.180          1             1
## 1159  20 30.590  50.590          2          <NA>
## 1160  32 41.100  73.100          6           5-6
## 1161  43 34.580  77.580          7          <NA>
## 1162  34 42.130  76.130          7          <NA>
## 1163  30 38.830  68.830          5           5-6
## 1164  18 28.215  46.215          1             1
## 1165  41 28.310  69.310          5           5-6
## 1166  35 26.125  61.125          4          <NA>
## 1167  57 40.370  97.370         10            10
## 1168  29 24.600  53.600          2          <NA>
## 1169  32 35.200  67.200          5           5-6
## 1170  37 34.105  71.105          6           5-6
## 1171  18 27.360  45.360          1             1
## 1172  43 26.700  69.700          6           5-6
## 1173  56 41.910  97.910         10            10
## 1174  38 29.260  67.260          5           5-6
## 1175  29 32.110  61.110          4          <NA>
## 1176  22 27.100  49.100          1             1
## 1177  52 24.130  76.130          7          <NA>
## 1178  40 27.400  67.400          5           5-6
## 1179  23 34.865  57.865          3          <NA>
## 1180  31 29.810  60.810          4          <NA>
## 1181  42 41.325  83.325          8          <NA>
## 1182  24 29.925  53.925          2          <NA>
## 1183  25 30.300  55.300          3          <NA>
## 1184  48 27.360  75.360          7          <NA>
## 1185  23 28.490  51.490          2          <NA>
## 1186  45 23.560  68.560          5           5-6
## 1187  20 35.625  55.625          3          <NA>
## 1188  62 32.680  94.680         10            10
## 1189  43 25.270  68.270          5           5-6
## 1190  23 28.000  51.000          2          <NA>
## 1191  31 32.775  63.775          4          <NA>
## 1192  41 21.755  62.755          4          <NA>
## 1193  58 32.395  90.395          9          <NA>
## 1194  48 36.575  84.575          8          <NA>
## 1195  31 21.755  52.755          2          <NA>
## 1196  19 27.930  46.930          1             1
## 1197  19 30.020  49.020          1             1
## 1198  41 33.550  74.550          6           5-6
## 1199  40 29.355  69.355          5           5-6
## 1200  31 25.800  56.800          3          <NA>
## 1201  37 24.320  61.320          4          <NA>
## 1202  46 40.375  86.375          9          <NA>
## 1203  22 32.110  54.110          2          <NA>
## 1204  51 32.300  83.300          8          <NA>
## 1205  18 27.280  45.280          1             1
## 1206  35 17.860  52.860          2          <NA>
## 1207  59 34.800  93.800         10            10
## 1208  36 33.400  69.400          5           5-6
## 1209  37 25.555  62.555          4          <NA>
## 1210  59 37.100  96.100         10            10
## 1211  36 30.875  66.875          5           5-6
## 1212  39 34.100  73.100          6           5-6
## 1213  18 21.470  39.470          1             1
## 1214  52 33.300  85.300          9          <NA>
## 1215  27 31.255  58.255          3          <NA>
## 1216  18 39.140  57.140          3          <NA>
## 1217  40 25.080  65.080          5           5-6
## 1218  29 37.290  66.290          5           5-6
## 1219  46 34.600  80.600          8          <NA>
## 1220  38 30.210  68.210          5           5-6
## 1221  30 21.945  51.945          2          <NA>
## 1222  40 24.970  64.970          5           5-6
## 1223  50 25.300  75.300          7          <NA>
## 1224  20 24.420  44.420          1             1
## 1225  41 23.940  64.940          5           5-6
## 1226  33 39.820  72.820          6           5-6
## 1227  38 16.815  54.815          3          <NA>
## 1228  42 37.180  79.180          7          <NA>
## 1229  56 34.430  90.430          9          <NA>
## 1230  58 30.305  88.305          9          <NA>
## 1231  52 34.485  86.485          9          <NA>
## 1232  20 21.800  41.800          1             1
## 1233  54 24.605  78.605          7          <NA>
## 1234  58 23.300  81.300          8          <NA>
## 1235  45 27.830  72.830          6           5-6
## 1236  26 31.065  57.065          3          <NA>
## 1237  63 21.660  84.660          8          <NA>
## 1238  58 28.215  86.215          9          <NA>
## 1239  37 22.705  59.705          4          <NA>
## 1240  25 42.130  67.130          5           5-6
## 1241  52 41.800  93.800         10            10
## 1242  64 36.960 100.960         10            10
## 1243  22 21.280  43.280          1             1
## 1244  28 33.110  61.110          4          <NA>
## 1245  18 33.330  51.330          2          <NA>
## 1246  28 24.300  52.300          2          <NA>
## 1247  45 25.700  70.700          6           5-6
## 1248  33 29.400  62.400          4          <NA>
## 1249  18 39.820  57.820          3          <NA>
## 1250  32 33.630  65.630          5           5-6
## 1251  24 29.830  53.830          2          <NA>
## 1252  19 19.800  38.800          1             1
## 1253  20 27.300  47.300          1             1
## 1254  40 29.300  69.300          5           5-6
## 1255  34 27.720  61.720          4          <NA>
## 1256  42 37.900  79.900          7          <NA>
## 1257  51 36.385  87.385          9          <NA>
## 1258  54 27.645  81.645          8          <NA>
## 1259  55 37.715  92.715         10            10
## 1260  52 23.180  75.180          7          <NA>
## 1261  32 20.520  52.520          2          <NA>
## 1262  28 37.100  65.100          5           5-6
## 1263  41 28.050  69.050          5           5-6
## 1264  43 29.900  72.900          6           5-6
## 1265  49 33.345  82.345          8          <NA>
## 1266  64 23.760  87.760          9          <NA>
## 1267  55 30.500  85.500          9          <NA>
## 1268  24 31.065  55.065          3          <NA>
## 1269  20 33.300  53.300          2          <NA>
## 1270  45 27.500  72.500          6           5-6
## 1271  26 33.915  59.915          4          <NA>
## 1272  25 34.485  59.485          4          <NA>
## 1273  43 25.520  68.520          5           5-6
## 1274  35 27.610  62.610          4          <NA>
## 1275  26 27.060  53.060          2          <NA>
## 1276  57 23.700  80.700          8          <NA>
## 1277  22 30.400  52.400          2          <NA>
## 1278  32 29.735  61.735          4          <NA>
## 1279  39 29.925  68.925          5           5-6
## 1280  25 26.790  51.790          2          <NA>
## 1281  48 33.330  81.330          8          <NA>
## 1282  47 27.645  74.645          6           5-6
## 1283  18 21.660  39.660          1             1
## 1284  18 30.030  48.030          1             1
## 1285  61 36.300  97.300         10            10
## 1286  47 24.320  71.320          6           5-6
## 1287  28 17.290  45.290          1             1
## 1288  36 25.900  61.900          4          <NA>
## 1289  20 39.400  59.400          4          <NA>
## 1290  44 34.320  78.320          7          <NA>
## 1291  38 19.950  57.950          3          <NA>
## 1292  19 34.900  53.900          2          <NA>
## 1293  21 23.210  44.210          1             1
## 1294  46 25.745  71.745          6           5-6
## 1295  58 25.175  83.175          8          <NA>
## 1296  20 22.000  42.000          1             1
## 1297  18 26.125  44.125          1             1
## 1298  28 26.510  54.510          3          <NA>
## 1299  33 27.455  60.455          4          <NA>
## 1300  19 25.745  44.745          1             1
## 1301  45 30.360  75.360          7          <NA>
## 1302  62 30.875  92.875         10            10
## 1303  25 20.800  45.800          1             1
## 1304  43 27.800  70.800          6           5-6
## 1305  42 24.605  66.605          5           5-6
## 1306  24 27.720  51.720          2          <NA>
## 1307  29 21.850  50.850          2          <NA>
## 1308  32 28.120  60.120          4          <NA>
## 1309  25 30.200  55.200          3          <NA>
## 1310  41 32.200  73.200          6           5-6
## 1311  42 26.315  68.315          5           5-6
## 1312  33 26.695  59.695          4          <NA>
## 1313  34 42.900  76.900          7          <NA>
## 1314  19 34.700  53.700          2          <NA>
## 1315  30 23.655  53.655          2          <NA>
## 1316  18 28.310  46.310          1             1
## 1317  19 20.600  39.600          1             1
## 1318  18 53.130  71.130          6           5-6
## 1319  35 39.710  74.710          6           5-6
## 1320  39 26.315  65.315          5           5-6
## 1321  31 31.065  62.065          4          <NA>
## 1322  62 26.695  88.695          9          <NA>
## 1323  62 38.830 100.830         10            10
## 1324  42 40.370  82.370          8          <NA>
## 1325  31 25.935  56.935          3          <NA>
## 1326  61 33.535  94.535         10            10
## 1327  42 32.870  74.870          6           5-6
## 1328  51 30.030  81.030          8          <NA>
## 1329  23 24.225  47.225          1             1
## 1330  52 38.600  90.600          9          <NA>
## 1331  57 25.740  82.740          8          <NA>
## 1332  23 33.400  56.400          3          <NA>
## 1333  52 44.700  96.700         10            10
## 1334  50 30.970  80.970          8          <NA>
## 1335  18 31.920  49.920          2          <NA>
## 1336  18 36.850  54.850          3          <NA>
## 1337  21 25.800  46.800          1             1
## 1338  61 29.070  90.070          9          <NA>
ggplot() +
  geom_point(data = inc_pca, 
             aes(x = age, 
                 y = bmi, 
                 color = pc1_decile_ch)) +
  theme_minimal()

inc_pca <- inc_pca %>% 
  mutate(pc2 = age - bmi) %>%
  mutate(pc2_decile = ntile(pc2, 10)) %>%
    mutate(pc2_decile_ch = case_when( 
    pc2_decile == 1 ~ "1",
    (pc2_decile == 5) | (pc2_decile == 6) ~ "5-6",
    pc2_decile == 10 ~ "10"
  ))

ggplot() +
  geom_point(data = inc_pca, 
             aes(x = age, 
                 y = bmi, 
                 color = pc2_decile_ch)) +
  theme_minimal()

inc_pca_pc1 <- inc_pca %>%
  group_by(pc1_decile) %>% 
  summarise(age_pc1 = mean(age),
            bmi_pc1 = mean(bmi))

inc_pca_pc2 <- inc_pca %>%
  group_by(pc2_decile) %>%
  summarise(age_pc2 = mean(age),
            bmi_pc2 = mean(bmi))

inc_pca_ggplot <- ggplot() +
  geom_point(data = inc_pca,
             aes(x = age, y = bmi)) + 
  geom_smooth(data = inc_pca_pc1,
              aes(x = age_pc1, y = bmi_pc1),
              method=lm,
              color="Blue", fullrange = F,
              size = 2
              ) +
  geom_smooth(data = inc_pca_pc2, 
              aes(x = age_pc2, y = bmi_pc2),
              method=lm, 
              orientation = "y", 
              color="Green", fullrange = F,
              size = 2
              ) +
  theme_minimal()

inc_pca_ggplot
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

ggplot() +
  geom_point(data = inc_pca, aes(x = pc1, y = pc2)) +
  theme_minimal() 

inc_pca <- inc_pca %>% 
  select(age, bmi)

inc.pca <- prcomp(inc_pca, 
                scale = T)

inc.pca$rotation
##           PC1        PC2
## age 0.7071068  0.7071068
## bmi 0.7071068 -0.7071068
data <- as.data.frame(inc.pca$x)

ggplot() +
  geom_point(data = data, 
             aes(x = PC1, y = PC2)) +
  theme_minimal() 

 

Задание 10. В финале вы получите график PCA по наблюдениям и переменным. Сделайте кластеризацию данных на нём по возрастным группам (создайте их сами на ваш вкус, но их количество должно быть не меньше 3)

inc_pca_ggplot
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

 

Задание 11. Подумайте и создайте ещё две номинативные переменные, которые бы гипотетически могли хорошо разбить данные на кластеры. Сделайте две соответствующие визуализации.

 

Задание 12. Давайте самостоятельно увидим, что снижение размерности – это группа методов, славящаяся своей неустойчивостью. Попробуйте самостоятельно поизменять дафрейм – удалить какие-либо переменные или создать их (создавайте только дамми переменные). Ваша задача – резко поднять качество вашего анализа PCA (при этом, фактически, оперируя всё теми же данными). Кратко опишите, почему добавление той или иной дамми переменной так улучшает PCA.